- Volume 12 Issue 1
The Box-Cox transformation is a well known family of power transformation that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Sample Entropy statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the maximum likelihood procedure, the procedure via artificial regression estimation, and the recently introduced maximization of the Shapiro-Francia W' statistic procedure is given. In addition, we generate a table for the optimal spacings parameter in computing the Sample Entropy statistic.
- Biometrika v.62 On Power Transformation to Symmetry Hinkley, D. V.
- American Statistician v.43 An Empirical Nonlinear Data-Fitting Approach for Transforming Data to Normality Lin, L. I.;E. F. Vonesh
- Biometrika v.52 no.3-4 An Analysis of Variance Test for Normality Shapiro, S. S.;M. B. Wilk
- Journal of the Royal Statistical Society, Series B v.38 no.1 A Test for Normality Based on Sample Entropy Vasicek, Oldrich
- Applied Statistics v.26 On Quick Choice of Power Transformation Hinkley, D. V.
- Biometrika v.48 no.1-2 Expected Values of Normal Order Statistics Harter, H. Leon
- The Annals of Statistics v.4 no.2 Asymptotic Results for Goodness-of-fit Statistics with Unknown Parameters Stephens, M. A.
- Biometrika v.64 Tests for Departure from Normality: Comparison of Powers Pearson, E. S.;R. B. D'Agostino;K. O. Bowman
- Journal of the American Statistical Association v.63 A Comparative Study of Various Tests of Normality Shapiro, S. S.;M. B. Wilk;H. J. Chen
- Classical and Modern Regression with Applications, Second Edition The Duxbury Advanced Series in Statistics and Decision Sciences Myers, Raymond H.
- Journal of the Royal Statistical Society, Series B v.26 An Analysis of Transformations Box, G. E. P.;D. R. Cox
- Journal of the American Statistical Association v.76 An Analyisis of Transformations Revisited Bickel, P. J.;K. A. Doksum
- Journal of the American Statistical Association v.67 no.337 An Approximate Analysis of Variance Test for Normality Shapiro, S. S.;R. S. Francia
- The Mathematical Theory of Communication Shannon, C. E.
- Journal of the American Statistical Association v.77 An Analysis of Transformation Revisited (Rebutted) Box, G. E. P.;D. R. Cox
- Journal of the Royal Statistical Society, Series B v.42 A Robust Method for Testing Transformations to Achieve Approximate Normality Carroll, R. J.
- Communications in Statistics- Simulation and Computation v.25 no.2 Estimating the Box-Cox Transformation via an Artificial Regression Model Halawa, Adel M.
- Annals of Mathematical Statistics v.33 Power Transformations to Symmetry Taylor, J. M. G.
- Communications in Statistics- Simulation and Computation v.28 no.1 Estimating the Box-Cox Transformation via Shapiro-Wilk W Statistic Rahman, Mezbahur